How to fit curve based on two related independent variables ?

Hello, I met this problem when doing curve fitting with 'fit' function, I wish get some help.

For independent variables, I have:

x=[1 2 3 4 5 6];
y=[1 1 1 2 2 2];

The dependent variable is:

z=[10 11 12 13 14 15];

My function is written as:

z=a*(x/y+x)

a is the coefficient to be evaluated. x and y varies but related, so x and y don't form a 2D plane. the result of 'x/y' in the function is actually supposed to be equivalent to 'x./y'.

I tried designating y as problem-depedent parameter (not working, as only one value is allowed for one parameter)

I tried using 'x./y' in the function, but it seems 'fit' still reads it as a 2D surface.

Please share your opinions on this problem, I have n't figure out the right way to do it yet. I appreciate a lot your help.

Sincerely

chen

Answer 1

[Ashok Kumar]

The problem can be simplified defining a new variable w = x/y.

Doing so you will get

z = aw+ax

Now it is simplified for the linear fit.

find a for given a and w to get the best fit.

x = [1 2 3 4 5 6];

y = [1 1 1 2 2 2];

z = [10 11 12 13 14 15];

w = x ./ y; % To Compute w = x/y

% To build the design matrix

X = [w', x'];

a = X \ z';

disp(['Estimated value of a: ', num2str(a)]);